Whenever the board of supervisors of any county finds by order or resolution entered upon its minutes that it is to the best interest of the citizens of said county for it so to do, that a public necessity therefor exists, and that said county would be benefited thereby, it is authorized and empowered in its discretion to cause to be constructed or reconstructed, at the expense of such county, such portion as it may elect of any public road lying in a contiguous county which extends from the county line of such county into such contiguous county, together with one or more connecting roads leading therefrom located in the contiguous county. The construction or reconstruction of the public road lying in a contiguous county which extends from the county line of such county into such contiguous county may be paid for out of county road funds, state aid road funds, or such other funds as may be available therefor. However, state aid road funds shall not be used to construct or reconstruct any connecting road located in the contiguous county, and the county constructing or reconstructing said connecting roads may pay therefor only from county road funds or such funds as may be available therefor other than state aid road funds. In the event state aid funds are used in connection with the exercise of the power and authority granted in this subsection, the state aid engineer's duties, responsibilities, and authority with respect thereto shall be the same as that provided by the law governing state aid projects. Before exercising any rights or authority granted in this subsection, the board of supervisors of the county proposing to take advantage of the authority herein contained shall secure the consent of the board of supervisors of the contiguous county, which consent shall be evidenced by an order or resolution of the board of supervisors of the contiguous county and spread upon its minutes.